1. The purple circle has two question marks (the left one is used in Spanish). Customer support is about answering lots of questions, so this is one of the reasons I used those symbols. For the name itself, I made a list of possible candidates, and really liked the simplicity of "Full Help". Also, it's close to some popular apps like Full Story and Full Contact.

2. For the web sockets, I was initially using Laravel Echo Server (https://github.com/tlaverdure/laravel-echo-server) (powered by Socket.io) and then switched to Laravel Websockets package (https://github.com/beyondcode/laravel-websockets) which is an implementation using PHP itself, making the requirements and installation even easier.